Solving the flatness problem with an anisotropic instanton in Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper proposes a novel solution to the flatness problem in cosmology within Hořava-Lifshitz gravity, utilizing an anisotropic instanton and the theory's deformed dispersion relations to set initial conditions.

Contribution

It introduces a new mechanism involving anisotropic instantons in Hořava-Lifshitz gravity to address the flatness problem, expanding the potential initial conditions for the universe.

Findings

The mechanism relies on anisotropic instantons respecting the same scaling.

It depends on deformed dispersion relations and energy equipartition.

The approach may be more general than the specific model presented.

Abstract

In Ho\v{r}ava-Lifshitz gravity a scaling isotropic in space but anisotropic in spacetime, often called anisotropic scaling with the dynamical critical exponent z=3, lies at the base of its renormalizability. This scaling also leads to a novel mechanism of generating scale-invariant cosmological perturbations, solving the horizon problem without inflation. In this paper we propose a possible solution to the flatness problem, in which we assume that the initial condition of the Universe is set by a small instanton respecting the same scaling. We argue that the mechanism may be more general than the concrete model presented here, and rely simply on the deformed dispersion relations of the theory, and on equipartition of the various forms of energy at the starting point.